Jökull - 01.12.1977, Page 14

very quickly, and hence their path is a straight
line whose horizontal and vertical components
are the prevailing wind, and the terminal velo-
city. The latter is described by the equations of
Stokes (laminar flow) or Newton (turbulent
flow).
If these two equations — those of Stokes and
Newton — are taken to describe the boundary
conditions for the fall of a particle in a viscous
medium, the distribution of maximum grain
size as a function of distance from the source,
for a given “eruptive vigour”, density of par-
ticle, and wind velocity, should describe a
straight line wliose slope should lie between
— i/2 (Stokes) and — 1 (Newton) on a logarith-
mic plot, i.e.:
Stokes: log d = — l/2 log s -f c
Newton: log d = — 1 log s + c
where d is the grain diamcter, and s the distance
from the source. Four variables are incorporat-
ed in the constant “c”: the wind velocity, the
viscosity of the air, the density of the grains,
and the “eruptive vigour”. They may be con-
siderecf reasonably constant for a given eruption
in this simple model if by "eruptive vigour”
the most vigorous phase of the eruption (usually
the initial part) is taken as representative. How-
ever, in interpreting natural samples it must
be expected that samples are non-representa-
tive such that the largest grain need not re-
present that of the equidistance curve from the
volcano and, especially for long-lived eruptions
and localities near to the eruption site, the
tephra may be the result of many asli showers
produced at variable eruptive vigour and wind
velocity. A line enveloping the uppermost points
for a given eruption (or eruption phase, if the
eruption is well known) is the representative
one for that eruption — the points falling be-
low are due to sporadic sampling or fluctuation
in the “energy of the environment”. Given re-
presentative samples the diagram should de-
scribe a family of straight lines of negative
slopes, in which tlie intercept at the ordinate
was in some measure proportional to “eruptive
vigour”, i.e. height of the volcanic cloud.
At the top of the diagram (Fig. 5) are marked
the chief volcanoes responsible for the tephras
on Bárdarbunga, and the Bárdarbunga samples
(diameter of largest grain vs. distance frorn
1 2 JÖKULL 27. ÁR
source, according to the j)resent interpretation)
are shown in bold asterisks in the diagram. In
general, since the Bárdarbunga samples are
small — the core diameter is 9 cm — the samples
should become increasingly representative witli
distance from the source. Hence, the two Katla
layers fit well with the reference samj)les K-1485.
The similarity of the two Askja samples may
indicate that they are representative, and that
their relatively fine grain size is related to that
particular tyj)e of eruption (Strombolian/Ha-
waiian). Conversely, the Grímsvötn and Kverk-
fjöll samjdes from Bárdarbunga are unlikely to
be representative owing to the nearness to the
respective volcanoes: The samples are too small
compared to grain size, and the grain size dis-
tribution may be affected by a horizontal balli-
stic comjronent in the eruption, i.e. if the
tephra is hurled out obliquely froni the crater
the ballistic effect is obsert'ed at least 30 km
away from the volcano, as evidenced by the
K-1360 data points in the diagram.
Estimates of the grain size characteristics of
the Bárdarbunga tephras are listed in Table I.
They were used in assembling the dej)th-age
model, to judge the “nearness” of a given tephra
to its source. Further work is in progress on the
grain morphology of the tephras.
Chemical characteristics
Of the 30 samples, 26 were mounted and the
glasses analyzed with the microprobe. In some
of the samples more than one distinct type of
glass was jrresent, resulting in the total of 31
analyses. In Table III the arithmetic means,
together with the analytical range, are reported.
In Fig. 6 TiO^ is plotted against the loga-
rithrn of P2O5 for the 31 analyses. The basaltic
glasses fall into three distinct groups, that may
be loosely termed olivine-tholeiitic (1.5—2%
TiO^), tholeiitic (2.7—3.2% TÍO2), and alkalic
(over 4% Ti02). Part of Bb 483 (V 1717) is
highly silicic (over 70% silica), and Bb 438
(? 1768) and Bb 196 (V 1887) are intermediate
in composition with about 60% and 53% silica,
respectively.
The analyses within the three basaltic groujrs
have been averaged, and are reported in Table
IV together with standard deviations. From
that Table it is evident that the three groups